Fluid foil lifting surface



Feb. 21, 1950 M. A. GARBELL 2,498,262

FLUID FOIL LIFTING SURFACE Filed Sept. 16, 1946 3 Sheets-Sheet 1 /l IFIGURE I 472 %M/J(INVENTOR.

Feb. 21, 1950 M. A- GARBELL FLUID FOIL LIFTING SURFACE 3 Sheets-Sheet 2Filed Sept. 16', 1946 FIGURE ZOEhumm SPANWISE SEMI-SPAN STATION ROOT I 3FIGURE 3 INVENTOR.

Feb. 21, 1950 Filed SECTION LIFT SECTION LIFT SBP 1945 3 Sheets-Sheet 5FIGURE 5 -4 LIJ ROOT SPANWISE- SEMI-SPAN 2 STATION 2 FlGURE U J 5 2 u.

u. m 0 U ROOT SPANWISE SEMISPAN STATION d.f4 INVENTOR.

Patented F eb. 21 1950 UNITED STATES PATENT (OFFICE-J Maurice A.G'arbll, San"Francisco, Calif, as-

signor, by direct and mesnc assignments, "of one-fourth to *Maurice A.Garbell,= Inc.,*San Francisco, Galif.,a corporation of California,andthree-fourths to GarbellResearch Foundation, San Francisco, Calif, acorporation of California Application September 16, -194.6-,-Serial-N0.697,281

1 This invention relates to the design and construction of surfaces tobedriven through a fluid, and -in particular through the air,- intendedto produce a'useful force component perpendicular t the relativevelocity of the fluid with respect -1948;-the general object-of which-isthe-attainment of good" stalling characteristics on lifting surfaces bymeans of anovel method-0f fluid-foil selection,"wherein the mean-linecamber-and if necessary the thickness ratio of one or more fluid foilsections interjacent "between the root and the tip'o'f the liftingsurface' are varied :from the respective values obtainable by straightline fairing between the-root'and tip sections by following the subjectmethodof :the said co-pending application.

The 'general' objects of the invention specified in the instantapplication are the attainment of good stalling characteristics, theelimination of violent rolling moments, the creation of stablemose-downpitchingmoments at the stall. the -niaintenance of adequatelateral 'control effectiveness, the reduction of the fluid-dynamic drag,and a reduction "of the resulting drag moment with respect-to the-rootofthe'lifting surface.

Another object of the invention specified-inthe iristant' application isthe attainmentof especiall'y high lifting-surface liftcoefficients inthose 'designs" in which engineering considerations other than thosepertaining solely to the control of stalling characteristics. perrnit Ythe "fluid-dynami- 'fluid foil sections are defi'ned' and explained-inthe subject specification of 5 this invention.

Other objects an'd advantages will hex-apparent from anexamiriati'on ofthe" drawings "accompan'ying the-instant application taken in -'con- 4junction with the following and in which:

Figure l shows aschem'atic perspective view of a lifting surfacedesignedand constructediaccbfding to theniethod outlined in the'subje'ct specification.

Figure 2illustrates the spanwise distribution of actually prevailingsection lift coefficients and the spanwis-e distribution of maximumattainable section lift coefficients on a typical lifting surfacedesigned and constructed'acconding t0 the sub- =ject method of thisinvention.

Figure 3 illustrates the typical --inception.iand growth of the :stallof alifting surface designed and constructed according to the subject:rnethod o'f'this invention. a V Figure 4 illustrates the procedureemployed in the finding of 'the optimum spa-nwise wlocation of the thirdcontrolled fluid-foil section in "a lifting surface designedwandconstructed: according to "the subject :method of this invention.

Figure 5 illustrates the spa-nwise"distribution sQf actually. prevailingsection lift cCOEfl'lClGIltS and the spanwise': distribution-,of-:maximum attainable section lift coefficients ion-a typicaliliftinjg :Sunface designed and constructed according to the sub.-

ject metnodbf this invention; :the' ":tip :sectionwof said liftingsurface having a thickness ra,tijo smaller than the optimum thicknessratio for lab,- .solutely maximum attainableesectioniliftrcoefi'le:cient for theseriesoftfiuidefoiIsectiQnsEemDIQyed in the liftingsurface.

'A preferred embodiment -.of this -:invention is described in thefollowing specification; thepbroad. .scope of the invention" isexpressed inthe claims concludingthe instantapplication.

The invention consists of =novelrmethodssand combinations of:methodsdescribed hereinafter, all of which contribute-to;produce;arsafeand rem-- cient lifting surface. :Referring' to theidrawingsiforamoresspecifidqdetails of the invention, FigureI'ISBI'VGStO illustrate ---the preferredsembodimentofithis.inuenti0n-,cc0msprisinga lifting surfacewith threerorrmorefelon- -trol1edfluid-foi1 sections, in which a section with a smallmean-line camber l'is IOCBLtBdiidU-th'fIfOOt rof the lifting 1 surface;.1 av section with: a: greater mean-line camber 3 is rlocated atfthetfiuidadyinamically eff ective -tip of the, lifting: surface aftheactual tip fairing ofthe lifting surfacermaycom- -prise a faired:three-adimensional'fibody without identifiable mean-line camber,whichzis =not-:.:of

any consequence in the application of theesu-b- .--ject' invention)-an-dione' or more interjacentysec- :tions 2 are E selected cfollowing@themethod outlined below, said .t-interiacent lfluidefoiI sectionshaving values" of'the:meaneline-fcamberc'at Mari -ance with theva1ues4"obtainablerat thez-respecs tive spanwise stations by-meanszofnstraight line fairing between the. fiuid-sfoil wsectionwlocatcdeatthe root and the fluid-foil section located at the tip of the liftingsurface, wherein the respective values of the mean-line camber of one ormore of the interjacent fluid-foil sections exceed the mean-line camberof the more highly cambered tip section. It shall be understood that thepreceding considerations apply to all types of lifting surfacesregardless of the respective thickness ratios of the root and tipsections. It shall also be understood that additional considerationsrelative to the respective thickness ratios of the various controlledfluid-foil sections are presented herein for lifting surfaces whereinthe thickness ratio of th root section is the greatest, and thethickness ratio of the tip section is the smallest, respectively, of anyfluid-foil section employed in the lifting surface.

Figure 2 illustrates the preferred manner in which this invention,through the employment of the aforementioned method of fluid-foilselection, achieves the establishment of a curvilinear polygon 5describing the spanwise distribution of maximum attainable section liftcoefficients, said curvilinear polygon being so shaped that it envelopsclosely the curve 6 describing the spanwise distribution of the actuallyprevailing section lift coefficients, except that beyond the spanwisepoint I at which the highest actually prevailing section liftcoefiicient occurs the maximum attainabl section lift coefficientexceeds substantially the actually prevailing section lift coefficient,so that the stall inception occurs near midsemispan, spreads moreprevalently inboardward and to a smaller extent outboardward as shown inorderly progression by curves l2, l3, l4, l5, and [6 in Figure 3, anddoes not involve the extreme tip of the lifting surface prior to thebreakdown of the fluid flow over the entire remaining lifting surface.As used herein the curvilinear polygon 5 describing the spanwisedistribution of maximum attainable section lift coefficients isestablished by the respective values of the maximum attainable liftcoefficients of the root section 9, the tip section 8, and the third oradditional control section II, and by the respective maximum attainablelift coefficients 5 of the sections obtained by conventional fairingbetween each pair of controlled sections 9--l I, ll-B, etc.

The curve 6 describing the spanwise distribution of the actuallyprevailing section lift coefficients at the maximum lift coefficient ofthe lifting surface is obtained by conventional methods ofexperimentally verified calculation for the desired lifting surface,taking into consideration the planform, effective aerodynamic washout,section lift-curve-slope characteristics, etc.

The term envelopment as used herein signifies the establishment ofcurvilinear polygon 5 on the convex side of the curve 6, wherein eachindividual branch 9-! l, I|--8, and so forth of the curvilinear polygon5 is tangent or nearly tangent to curve 6.

The following specification outlines the method employed in the designof the subject lifting surface of this invention, whereby to select themost opportune values of fluid-foil section mean-line camber andfluid-foil section thickness ratio required to achieve the objects ofthe instant invention:

To apply the subject method of this invention it is actually necessaryto know only th planform of the lifting surface and the desired stallpattern. Inasmuch as practical considerations other than thosepertaining solely to the control of the stalling characteristicsordinarily predetermine certain design parameters of the liftingsurface,

4, preferred embodiments of the subject method of this invention arehereinafter explained for two typical combinations of predetermineddesign parameters:

In the first typical configuration the following design parameters, forexample, are assumed to be given a priori: (a) the planform of thelifting surface, based on structural and practical designconsiderations; (b) the series of fluid-foil sections to be employed,based on high-speed and other performance requirements; (0) the maximumpermissible effective aerodynamic washout, based on drag considerationsand structural bendingmoment limitations; ((1) the thickness ratio ofthe fluid-foil section at the root, based on the critical-Mach-Numberrequirements and structural weight considerations; (e) the thicknessratio of the fluid-foil section at the tip, based on practical spacerequirements for control-surface balances, etc; (f) the maximummean-line camber of any fluid-foil section on the lifting surface, basedon drag and pitching-moment limitations.

The subject method of this invention is employed firstly to design thelifting surface without any effective aerodynamic washout, that is, withthe three or more controlled fluid-foil sections placed at such an angleof incidence with respect to the reference chord plane of the liftingsurface that the said fluid-foil sections operate at their respectivezero-lift angles of attack when the entire lifting surface operates atits angle of attack for zero overall lift.

Based on fundamental experimental wind-tunnel data available for thepreselected series of fluid-foil sections, graphs are plotted showingthe variation in the maximum attainable section lift coefficient versusthe mean-line camber, thickness ratio, and Reynolds number,respectively; similar graphs are plotted showing the variation in thesection zero-lift angle of attack versus the mean-line camber, thicknessratio, and Reynolds number, respectively.

For the spanwise location of the third and additional controlledsections 2 and II, the subject method of this invention utilizespreferably locations between the spanwise point of the highest actuallyprevailing section lift coefficient I and the spanwise point locatedtwice as distantly from the tip 8 as point 1, with a preferable optimumat the point H, where the tangent to the inboard portion of the curve ofspanwise dis-' tribution of the actually prevailing section liftcoefficients 1, 8 intersects the horizontal tangent l 9 to the samecurve, as shown in Figure 4.

It will be understood, however, that inescapable practical designconsiderations may require that the additional controlled sections 2 andll be placed at spanwise stations located inside power plant nacelles orat those spanwise stations where the lifting surface is mechanicallyjointed for sudden changes in planform taper, or sweep-back, as is thecase in craft with removable or foldable outboard panels.

The thickness ratio obtainable at the third section II is calculated bystraight-line interpolation between the root section and the tip sectionor is determined by such structural or other criteria of differentnature as may be considered to prevail. However, the subject method ofthis invention teaches that best results are achieved if the thicknessratio of the tip section 3 is smaller than the optimum section thicknessratio for absolutely maximum attainable section lift coefficient of thefluid-foil series chosen, and if the thickness ratio of the thirdsection} and.- l;lischosen'.edualzto/onsligl'it 1y greater than thesaidioptimum"thicknessgratio; sothat the optimum thickness ratiooccurseither atwthe third. section 2 and II or. at aspanwise location 2|near thepoint 22 of highest actually prevailing section liftcoefiicient.

The; approximate maximum attainable lift c0.- efllcient oftheentirelifting surface for. appropriategvalues. of the. Reynoldsnumber is estimated.

for example by dividing the. maximum attain.- ablesection liftcoefficient of the third" fluide foil. section (obtained from theaforementioned; wind-tunnel data for the selected values of thesectionthickness ratio and the maximum permis sible-mean line camber) by thehighestspanwisa value of the additional section lift coefficient (as.defined in Army-Navy-Commerce Manual ANC-1(1) entitled Spanwise Air-LoadDistribution), as follows:

C; of interjacent section max lmu in hilhesr and byrepeating thisoperation with checks of the Reynolds number of the said most highlycambered interjacent section as. specified in the.

co-pending application, until the maximum at tainable lift coefficientof the lifting surface. is accurately determined.

The spanwise distribution 6 of the actually prevailing section liftcoemcients is then calculated for the maximum liftcoefficient Cr of theentire lifting surface, following oneof the. conventional calculationmethods.

For the Reynolds number and the pro-selected. thickness ratio of the tipsection, the required. value of the mean-line camber is determined;

from the graph showing. the experimentally measured variation of themaximum. attainable.

section lift coefficient with varying. mean-line. camber, selecting thatvalue ofv the mean-line camber that produces av maximum. attainable...

section lift coefiicient 8i substantially equal to. the highest actuallyprevailing section lift coefll; cient'l;

For the Reynolds number and the pre-selected. thickness ratio of theroot section, the required. value ofthe. mean-line camber is determinedfrom the graph showing the experimentally measured variation ofthe'maximum attainable. sectionlift coefiicient with varying mean-line.cam-- ber, selecting that value. of the mean-line, cam.-

ber that-produces a maximum attainable section, lift-coefficient 9 equalto or slightly superiorv to.

the section lift coeflicient actually prevailing" over the root'section.

From the foregoing, it will be readily seen.

that. the lifting surface obtained by the invention; and defined by thecurvilinear polygon embodies the combination of a fluid-foil section.

I" or- 9 having the smallest mean-line camber at the root afiuid-foilsection 3 or. 8 having a great-.

ermean-line camber at the tip, and one orv more interjacent controlledsections 2 or ll. having values of the mean-line camber at variance.

with the values 4 obtainable at the respective spanwise stations bymeansof straightlinefai'ring between the root section and the tipsection, wherein the mean-line camber of the third;

or an additional interjacent controlled section exceeds the mean-linecamber of the morehighly cambered tip section, while avoiding the.uncle.-

sirablenefl'ects ofzany materlalaamountzofiaerodys.

namicawashin:

If; forgreasonszother than: those pertaining solelystothe.control-:of*stalling characteristics, wash I outx-is desired,aasmall' amount: of. effective" aerodynamiczwashout is.introduced, /2 to1 in eachstep: of; the: application; of the method, wherein theitotalieffective. aerodynamic: washout is distributedp-in appropriate:fashion between the con trolled sections .andrwherea the. total: washoutis.

lessithan the. maximum; permissible washout. as definedimthe aforesaidinitial design assumptions; The entire. heretoforespecified' procedure.

including the establishment. of a curve 6' con fornringzto. the-washout;chosen is then repeated forrztl'ie selected: amount. of reflectiveaerodynamic washout; until the desired results as illustratedilCh'FIglH-ES: 2 and; 3, are attained while satisfying.

the; aforesaid; requirementsaof difierent nature.

Atypical} example of:=the: application of the principles of.this-invention to one. well-known: type of lifting. surface. is asfollows: Here we:

assume a planformtaperratio of-three to one, anuaspect. ratio of ten; atotal. effective aerodynamic. washout: of zero. degree, a section thickness ratio-tapering linearlyfrom 22'per centtat. the.:roo.t to: 15 percent at thetip, the utiliza tion of 63- series NACA low-drag fluid-foil:

sections,..a; mean-line. camber of the. mosthighly cambereda. controlledsection. .21: characterized by an:.idea11-lift coefficient C1 equal to.0:4. The term. ideal lift'coefficient is to be interpreted315;.(18fihfld bythe. National Advisory Committee for. Aeronauticsnomenclature and is herein used? as:. a; parameter characteristic of themean-line. camberzof a. fluid-foil section. Calculationsbasedonconventionalmethods will indicate that a lift.- ing;-.surface= having:the above general designparameters .will; experience; at .its maximumresult?- antzli-ft: coefficient; adistributi'onpf section lift-cm.

efficients as illustratedin. curveafi;

Following the procedures 'hereinbefore de-- scribed, we. achieve in the:above-outlined con-. struction the: desirablestalling= characteristics:taughta by this invention; by. placing; the most:

highlywambered. controlled sectionat a:. station approximately.- 70' percentof .the semi-span from the;ro.ot;andiwith an; effective'aerodynamic. wash-- out; ofczero; degree withrespect' to the root sec.-

tion and": through: the use. of mean-line. camber.-

ofgthelrootzsection'. I.. characterized by an "ideal lift coefficientC15 equal; to: 0:1,.and a mean-line camber of the tip section 3characterized by an ideal lift coefficient C1 equal to 0.35.

In this structural example the mean-line camber of; theinterjacentcontrolled section 2 is bodiedin various devices wherein thethicknessgreater than that of the root sect-ion l and of" the tipsection3; and hence greater than that of the interpolated section 4 obtainableat-the n per cent semi-span station: by -means"ofstraight-linefairingbetween'sections I and 3, and whichaccomplishesthe envelopment' of curvesfi by the I curvilinear polygon'5.

It will be" fully appreciated by those skilled in thisa'art that. theinvention may bereadily emratio of-the interjacent section 2 isvaried'from that obtainable through straight+line fairing be-..

tween root: section. Land-tip. section 31in. order to--facilitate theattainment. of: the objectives of thisainventionwith the smallestpossible range of.v a1ues --of section mean-line camber.

The. second typical; configuration differs. from. the, first, in\, thattwov interiacentg SBCtiODSl 2a may be.-z.;uti 1ized. Hence, the.following: design pas.

rameters are assumed tobe given: a priori: (a) The plan form of thelifting surface; (b)- the series of fluid-foil sections to be employedand their fluid-dynamic characteristics; the maximum permissibleeffective aerodynamic washout; (d) the thicknessratios of the fluidfoilsection at the root and of the fluid-foil section at the tip,respectively; (e) the maximum mean-line camber to be assigned to anyfluid foil section on the lifting surface.

The number of interjacent controlled fluidfoil. sections, in this case,is not limited. The following representative specification applies tothe case of two interjacent' controlled fluid-foil sections; however,the reasonings specified therein are obviously usable in the design oflifting surfaces with a different number of interjacent controlledsections. Here it will be understood that the values of the mean-linecamber. of one or more of the interjacent controlled sections 2 aregreater than that of the more highly cambered tip section 3, while oneor more of the remaining interjacent controlled sections 2 may be eithergreater or smaller thanthat of the aforementioned tip section 3,depending on the range of section thickness ratios encountered betweenthe root and the tip of the lifting surface.

In this case the instant method teaches that the optimum spanwiselocation for the interjacent fluid-foil section having the greatestmeanline camber is in the vicinity of the spanwise station carrying thehighest actually prevailing section lift coefficient 1, and that theoptimum spanwise location for the second interjacent' fluid-foil sectionis point IT, where the tangent. at the root to the curve of spanwisedistribution of the actually prevailing section lift coefiicients l8intersectsthe horizontal tangent [9 to the same curve, as shown inFigure 4. The instant method also teaches that best stallingcharacteristics are obtained by assigning to the two or more interjacentfluid-foil sections valuesof the'i section thickness ratio that, for theseries of fluid-foil sections selected, yield the absolutelymaximumattainable section lift coefficients.

The approximate maximum attainable lift coefficient of the entirelifting surface is estimated by dividing the maximum attainable sectionlift coefficient of the most highly cambered fluid-foil section by thehighest spanwise value of the additional section lift coefficient in a,manner substantially similar to that previously outlined. s

,The spanwise distribution of the actually pre-, vailing section liftcoefficients 23 is then calcu lated for the maximum lift coefficient ofthe en-. tire lifting surface as previously outlined.

For the Reynolds number of the additional interjacent fluid-foilsection, preferably located at the spanwise station ll abovedefined, therequired value of the mean-line camber and if neeessary the thicknessratio is determined substan-. tially as outlined for the fluid-foilsection II in the co-pending application.

The value of the mean-line camber of the fluid foil section located atthe tip of the lifting surface is not of consequence in the applicationof the subject method of this invention, pro-- vided that the maximumattainable section lift coefficients represented by the curved segmentconnecting 1.points 2 2 and 20 Figure remains POL subst'antiallyabovethe curve of actually 'p'r'e vailing section lift coeflicients 23; 5 cIf the designer intends to achieve positivestall' inception in ace'rtainspanwise panel of the lifting surface, the subject method of thisinvention specifies that in either of the aforedescribed designprocedures the mean-line camber and thickness'ratios, as well as thespanwise location, of the sections comprised within or adjacent to thepanel forwhich stall inception is desired be so selected that within thestall inception panel the curve of maximum attainable section liftcoefficients lies slightly below the curve of actually prevailingsection lift coefficients, without modifying the aforedescribedrelationship of the maximum attainable section lift coefiicients and theactually prevailing section lift coefficients on the remainder of thesemispan of the lifting surface outside of the stall-inception panelproper.

"If, 'in any of the aforedescribed cases, the lift-, ing surface underconsideration is modified by"- excrescences such as, for example,power-plant nacelles, or flaps that modify the local zero-lift angle andthe local maximum attainable section lift coefficient, the calculationof the maximum attainable section lift coefiicients and of the effectivewashout at the various spanwise stations takes due account of theeffects of these modifica-f tions by introducing equivalent values ofthe effective washout and section mean-line camber into the subjectmethod of this invention.

Uponcompletion of the procedure outlined for the subject method of thisinvention, the zero-. lift angles of the fluid-foil sections selectedthus-f" 1y are determined for their respective mean-line stallingcharacteristics of lifting surfaces designed and constructed accordingto the subject method of this invention are directly attributable tothe.

u'se of three (or more) controlled fluid-foil sections selectedaccording to the hereinbefore speci fled method of this invention, andto the afore-.; described method employed in the design of such:

lifting surfaces.

This invention accomplishes an important im provement in the art, andthe discoveries herein disclosed are of great value to all types ofaircraft (as well as to craft operating in other fluids), throughouttheir entire operating range, and especially in the critical low-speedoperation where steadiness of lift and lift variation, stability of thecraft, control effectiveness, and smooths,

ness and stability of control forces are of vital importance for thesafety and efliciency of the craft; also in violent maneuvers at highspeeds.

when high liftingsurface lift coefficients coml A lifting surface withthree or more 76 ti'olled fluid-foil section's, in'which the first section with a small mean line' camber is'located at the root, the secondsection with greater meanline camber is located at the fluid-dynamicallyeffective tip, and the third or additional fluidfoil sections arelocatedat stations interjacent between the root and the tip, wherein the valuesof the mean-line camber of the interjacent fluidfoil sections are atvariance with the values of the mean-line camber obtainable at therespective'spanwise stations by means of straight-line fairing'betweenthe fluid-foil section located at the root of the lifting surface andthe fluid-foil section located at the tip of the'lifting surface, andwherein the mean-line camber of one or more of the interjacentfluid-foil sections exceeds the mean-line camber of the more highlycambered 'tip section, said three or more controlled fluid-foil sectionshaving values of the mean-line camber selected in such manner that theresulting spanwise distribution of maximum attainable section liftcoefficients of the three or more controlled sections forms acurvilinear polygon enveloping a curve representing the spanwisedistribution of section lift coefficients prevailing at the maximumattainable lift coefiicient of the lifting surface, for a given planformand discarding the effect of any material amount of aerodynamic washin.

'2. A lifting surface with three or more controlled fluid-foil sectionsadapted to provide stall inception within a predetermined interval ofspanwise stations, in which the first section with asmall mean linecamber is located at the root, the secondsection with greater mean-linecamber 'is located at the fluid-dynamically effective tip,-and thethirdor'additional fluid-foil sections are located at stationsinterjacen't between the root and the tip, wherein the values of themeanllne camber of the interjacent fluid-foil sections are at varianceWith'the values of'the mean-line camber obtainable attherespectivespanwise sta tions by means of straight-line fairingbetween the fluid-foil section located at the root of the liftingsurface and'thefiu'id-foil'section'located at the tip of the liftingsurface, and wherein the meanline camber of one or more of theinterjacent fluid-foil sections exceeds themean-line camber of themore'hi'ghly cambered tip section, said' three or more controlledfluid-foil sections having values of the mean-*ilne camber selected insuch manner that the resulting spanwise :distribution of maximumattainable section lift coe'fiicien'ts' of the-three or more controlledsections form-s acurvilinearpolygon enveloping a curve representing thespanwise distribution of section lift coefli'cien'ts prevailing atthe'maximum attainable lift coefficient of the lifting surface, *for agiven planform and discardingthe efiectof any material amount ofaerodynamic washin, and thatthe said'polygon representing the resultingspanwise distribution of maximum attainable section lift coefficients beso shaped that the first intersection with the curve representing thespan- Wisewdistribution of'sprevailing section lift coefficients'occursinithatinterval of spanwise stationsifor which r'stall inception is ':tobe obtained.

A ilifting surface with-three or "more controlledfluid foilisections, inwhich the first section withra small mean-"line camber and greatestthickness ratio isilocated at the root, the second section with greatermeanlinecamber: and smallesttthicknessratio is located at thefluid-dynamically'iieffective tip,'rand the third or additional valuesofithe thickness .ratio of the interjacent fluid-foil sections aregreater than the values or tionilocated at the tipof'thelifting surface,and

wherein the mean-line camber of one or more -01 the interjacentfluid-foil sections exceeds the mean-"line camber of themorehighlycambered tip section.

4. A lifting surface with three or more controlled fluid-foil sections,in which the first'section W'ith'asmall mean-line camber is located atthe root,the second section with greater meanline 'camber is "located atthe fluid-dynamically effective tip, and the third or additionalfluidfoil sections are located at stations interja'cen't between theroot and the tip, wherein the values of the thickness ratio of theinterjacent fluidfoil sections are at variance with the values er thethickness ratio obtainable at the respective spanwise stations 'by meansof straight-linefairin'g between the "fluid-foil section located at= theroot' o'f the lifting'surface and the fluid-foil section located -at thetip o'f'the lifting surface, and

planform -andxdiscarding the effect o'f'any mate-' rial amount ofaerodynamic washin.

*A liftingsurface with three or more *controlled fluid-"foil L sectionsadapted to provide stall inception within a predetermined interval ofspanwise' stations, in which the first section with a:small-mean-linecamber is located at the=root. the .second section with greatermean-line camber'is'located'at the fluid-dynamically effective tip,and-the third or additional fluid-foil sections are located at'I'station's interjacent between the root -an'dthe tip, wherein thevalues of the thickness 'ratio of the interjacent fluid-foil sectionsare at varian-ce with the values of the thickness ratio obtainable atthe respective spanwise stations Eby "means of straight-line fairingbetween the "fluid-foil' section'located at the root of the liftingsurface aridthe fluid-foil section located at' thetip of the liftingsurface, and whereinthe mean-line camber of one or more of theinterjacent fluid-"foil sections exceeds the 'mean-line camber of themore 'higlilycam'beredtip section, saidthree or more controlledfluid-foil sections having' valuesof themean-line camber and thethicknessratio selected'in such manner thatthe resulting spanwisedistribution of maximum attainabl-e section lift coefficients ofthe'three "or more-controlled sections forms'a curvilinearpolygonenveloping a curve representing the spanwise distribution -of sectionlift coefficients prevailing at themaximum attainable lift coefficientof the lifting surface, for a given planforrn and discarding the effectof ,any material amount'of aerodynamic washin, andthat thesai'dresultingintersection with the spanwise distribution "ofprevailingsection lift coefficients occurs in that interval of spanwise stationsfor which stall inception is to be obtained.

6. A lifting surface with three or more controlled fluid-foil sections,and having a highest actually prevailing section lift coefficient at apre determined spanwise station, in which the first section with a smallmean-line camber is located at the root, the second section with greatermeanline camber is located at the fluid-dynamically effective tip, andone of the interjacent fluidfoil sections is located near a spanwisepoint where a tangent to the inboard portion of the curve representingthe spanwise distribution of actually prevailing section liftcoeificients, for a given planform and discarding the effect of anymaterial amount of aerodynamic washin, intersects a substantiallyhorizontal tangent to the highest point of the same curve, wherein thevalues of the mean-line camber of the interjacent fluid-foil sectionsare greater than the values of the mean-line camber obtainable at therespective spanwise stations by means of straightline fairing betweenthe fluid-foil section located at the root of the lifting surface andthe fluidfoil section located at the tip of the lifting sur-- face, andwherein the mean-line camber of one or more of the interjacentfluid-foil sections exceeds the mean-line camber of the more highlycambered tip section.

'7. A lifting surface with three or more controlled fluid-foil sections,and having a highest actually prevailing section lift coeificient at apredetermined spanwise station, in which the first section with a smallmean-line camber and greatest thickness ratio is located at the root,the second section with greater mean-line camber and smallest thicknessratio is located at the fluid-dynamically effective tip, and one of theinterjacent fluid-foil sections is located near a spanwise point where atangent to the inboard portion of a curve representing the spanwisedistribution of actually prevailing section life coefii-' cients, for agiven planform, and discarding the effect of any material amount ofaerodynamic washin, intersects a substantially horizontal tan-' gent tothe highest point of the same curve,

wherein the values of the thickness ratio of the interjacent fluid-foilsections are greater than the values of the thickness ratio obtainableat the respective spanwise stations by means of straight-line fairingbetween the fluid-foil section located at the root of the liftingsurface and the fluid-foil section located at the tip of the liftingsurface, and wherein the mean-line camber of one or more of theinterjacent fluid-foil sections exceeds the mean-line camber of the morehighly cambered tip section.

8. A lifting surface with three or more controlled fiuid-foil sections,and having ahighest actually prevailing section lift coeflicient at apredetermined spanwise station, in which the first section with a smallmean-line camber is located at the root, the second section with greatermean-line camber is located at the fluiddynamically effective tip, andtwo of the interjacent fluid-foil sections are located respectively nearthe spanwise station of highest actually prevailing section liftcoefilcient and near a spanwise point where a tangent to the inboardportion of a curve representing the spanwise distribution of actuallyprevailing section lift coefih cients, for a given planform anddiscarding the effect of any material amount of aerodynamic washin,intersects the horizontal tangent to the highest point of asubstantially same curve, wherein the values of the mean-line camber ofthe interjacent fluid-foil sections are greater than the values of themean-line camber obtain able at the respective spanwise stations bymeans of straight-line fairing between the fluid-foil section located atthe root of the lifting surface and the fluid-foil section located atthe tip of the lifting surface, and wherein the mean-line camber of oneor more of the interjacent fluid-foil sections exceeds the mean-linecamber of the more highly cambered tip section.

9. A lifting surface with three or more con-- trolled fluid-foilsections, and having a highest actually prevailing section liftcoeflicient at a predetermined spanwise station, in which the firstsection with a small mean-line camber and greathorizontal tangent to thehighest point of the same curve, wherein the values of the thicknessratio of the interjacent fluid-foil sections are greater than the valuesof the thickness ratio obtainable at the respective spanwise stations bymeans of straight-line fairing between the fluidfoil section located atthe root of the lifting surface and the fluid-foil section located atthe tip of the lifting surface, and wherein the meanline camber of oneor more of the interjacent fluid-foil sections exceeds the mean-linecamber of the more highly cambered tip section.

10. A lifting surface with three or more controlled fluid-foil sections,in which the first section with a small mean-line camber and greatestthickness ratio is located at the root, the second section with greatermean-line camber and smallest thickness ratio is located at thefluid-dynamically effective tip, and the third or additional fluid-foilsections are located at stations interjacent between the root and thetip, wherein the values of the thickness ratio of the interjacentfluid-foil sections are smaller than the values of. the thickness ratioobtainable at the respective spanwise stations by means of straight-linefairing between the fluid-foil section located at the root of thelifting surface and the fluid-foil section located at the tip of thelifting surface, and wherein the mean-line camber of one or more of theinterjacent fluid-foil sections exceeds the mean-line camber of the morehighly cambered tip section.

11. A lifting surface with three or more controlled fluid-foil sections,and having a highest actually prevailing section lift coemcient at apredetermined spanwise station, in which the first section with a smallmean-line camber and greatest thickness ratio is located at the root,the second section with greater mean-line camber and smallest thicknessratio is located at the fluid-dynamically effective tip, and one of theinterjacent fluid-foil sections is located near aspanwise point where atangent to the inboard portion of a curve representing the spanwisedis--v tribution of actually prevailing section'lift co-l eflicients,for a given planform and discarding the effect of any material amount ofaerodynamic washin, intersects a substantially horizontal tangent to thehighest point of the same curve, wherein the Values of the thicknessratio of the interjacent fluid-foil sections are smaller than the valuesof the thickness ratio obtainable at the respective spanwise stations bymeans of straight-line fairing between the fluid-foil section located atthe root of the lifting surface and the fluid-foil section located atthe tip of the lifting surface, and wherein the mean-line camher of oneor more of the interjacent fluid-foil sections exceeds the mean-linecamber of the more highly cambered tip section.

12. A lifting surface with three or more controlled fiuid-foil sections,and having a highest actually prevailing section lift coefiicient at apredetermined spanwise station, in which the first section with a smallmean-line camber and greatest thickness ratio is located at the root,the second section with greater mean-line camber and smallest thicknessratio is located at the fluid-dynamically effective tip, and two of theinterjacent fluid-foil sections are located respectively near thespanwise station of highest actually prevailing section lift coefficientand near a spanwise point where a tangent to the inboard portion of acurve representing the spanwise dis- 14 tribution of actually prevailingsection lift coefficients, for a given planform and discarding theefiect of any material amount of aerodynamic washin, intersects asubstantially horizontal tangent to the highest point of the same curve,wherein the values of the thickness ratio of the interjacent fluid-foilsections are smaller than the values of the thickness ratio obtainableat the respective spanwise stations by means of straight-line fairingbetween the fluid-foil section located at the root of the liftingsurface and the fluid-foil section located at the tip of the liftingsurface, and wherein the mean-line camber of one or more of theinterjacent fluidfoil sections exceeds the mean-line camber of the morehighly cambered tip section.

MAURICE A. GARBELL.

REFERENCES CITED The following references are of record in the file ofthis patent:

UNITED STATES PATENTS Number Name Date 1,547,644 Cronstedt July 28, 19251,817,275 Soldenhoif Aug. 4, 1931 1,890,079 Focke Dec. 6, 1932 2,441,758Garbell May 18, 1948

